One of Kirby's possible Stone transformations is based on a Thwomp, using the blue design from Super Mario 64. A Thwomp also appears as a trophy using its main design which originates from Super Mario Bros. 3.

Thwomps spend most of their time suspended in midair, waiting. When Mario passes below, they crash down with amazing speed. As you may guess from their appearance, they're heavy and solid enough to make any attack on them futile. Small ones are called Thwimps: despite their weight, they often form groups and bounce around.

You can't reason with a Thwomp. If you get close enough to try, it will just drop down to block your path. In fact, you can count on Thwomps to always do exactly that—they've gotten really good at it. A Koopa I know swears they work great as a home-security system...

Have you ever wondered what it would be like to have a Thwomp of your own? If anyone tried to break into your house, it would just go "THWOMP!" right on their head. Yep, a Thwomp would make a great home-security system. Unfortunately, they're not available in shops. Sad times.

Thwomp makes its debut as an Assist Trophy. It behaves exactly as it does in Mario platformer games: it hangs in the air, and falls down when characters pass under it. Training Mode describes the Assist Trophy: Squishes opponents caught beneath it. Can't be KO'd.

As in SSB4, the modern Thwomp design appears as one of Kirby's possible Stone transformations.

Thwomp's Assist Trophy reveal is very similar to King K. Rool's fighter reveal. While King Dedede was disguised as K. Rool, only to get smacked by him later, Kirby follows suit by using Stone to take the form of Thwomp, only to get hit by a real one.